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If you realize that you can't do FTL and you still want to explore the stars a generation ship is your only option.

Sure it won't do you much good, but a descendant may get to see something.

How fast could such a ship travel as a fraction of the speed of light. Given our current understanding of physics?

I guess you'd need to consider fuel for acceleration and slowing down. If you can get more fuel on the way. Risks of going too fast (radiation, debris) and who knows what else.

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closed as primarily opinion-based by JBH, Mark, sphennings, L.Dutch, Vylix Oct 6 '17 at 4:52

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ I'm voting to close this question as off-topic because it should be migrated to physics.SE $\endgroup$ – JBH Oct 5 '17 at 21:43
  • $\begingroup$ I think there is more WB than phisics. You have to think about what can practically be done not what is phisically possible $\endgroup$ – Jeremy French Oct 5 '17 at 21:50
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    $\begingroup$ If this question hasn't already been answered by physicists (both from a scientific standpoint and from a practical standpoint) I'll proverbially eat my proverbial hat. $\endgroup$ – JBH Oct 5 '17 at 21:52
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    $\begingroup$ Not a physics question, simply too broad. The maximum possible speed of a generation ship depends on what assumptions you make about its capabilities and the environment it will be traveling through. $\endgroup$ – Mark Oct 5 '17 at 23:22
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    $\begingroup$ @JBH Generation ships aren't strictly speaking the province of physics. Expect to Physics SE to either close it or migrate it to, surprise, WB SE. Perhaps one of the space related SE's might be interested. But it can be tackled here. There are previous generation ship questions. $\endgroup$ – a4android Oct 6 '17 at 1:17
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Since the OP is asking about generation ships as the preferred method for exploring the cosmos, it is possible to apply a combination of logic and imagination to work out the maximum speed of a generation ship.

The nearest planetary system is Proxima Centauri which is 4.243 light years distant. Assuming a generation ship will arrive at Proxima Centauri when the next generation is old enough to explore the system. If the average age of the primary generation is, say, thirty years. They will old enough and well trained enough to run the ship on its voyage. They will raise their children to also run the ship and be able to explore another planetary system. Therefore, it's not unreasonable to assume this second generation will have an average age of, say, thirty. The first generation will now be on average, sixty years plus.

This establishes our generation ship has travelled to Proxima Centauri in thirty years at a minimum. It's possible to add a few years, but at 30 years flight time this gives the fastest possible passage of a journey to Proxima Centauri.

This yields an average velocity of 14.143 percent of lightspeed (psol) or 42,430 km/s. Now this calculation neglects acceleration time. Therefore, the actual maximum velocity will be higher than the average. If this was pushed up to, say, fifteen (15) percent of lightspeed, then the time for acceleration can be subsumed into the average velocity.

There are numerous discussion of interstellar travel that assume this will only take place at velocities of one percent of lightspeed (3,000 km/s). This is based on factors concerning the amount of energy required to accelerate a vehicle to close to lightspeed and the mass rations involved. All of which are prohibitive.

At one psol, a generation ship take 424.3 years to reach Proxima Centauri. But allowing for an acceleration phase at one centimetre per second squared which it take ten years to attain one psol plus a further deceleration phase at its destination, this add an additional decade flight time. This means a total trip time of 434.3 years.

In summary, the maximum speed for a generation ship to travel to Proxima Centauri, our nearest planetary system, wi1l be of the order of fifteen psol or 0.15 c. While more realistic generation ships can be expected to have velocities around one psol and to take more generations to reach their destination.

NOTE:

The unit of psol (percentage of the speed of light) was devised by James Strong in his book, Flight to the Stars: An Inquiry into the Feasibility of Interstellar Flight (1963).

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    $\begingroup$ It would be nice to find out why my answer was downvoted. If its logic or reasoning is flawed, I'd certainly like to know. Then I can edit or improve the answer. $\endgroup$ – a4android Oct 6 '17 at 4:38
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298 792 458 m / s

In a vacuum you can approach the speed of light, but once you reach the speed of light energy becomes matter.

So basically take the speed limit and reduce the velocity by some number.

In all reality though it would take a considerable amount of energy to reach this speed and a considerable amount more to maintain it. Space is dusty and that dust would likely provide some friction. You will also need to expend energy repelling that dust from ripping through your ship as you drive through it.

cool fact for you though, the faster one goes the slower their perception of time becomes. So if you approach the speed of light, what your people perceive as 1 year of flight is really 100 years in normal time. Obviously my ratio is fudged as an example but the real mathematically determined results can be just as dramatic.

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  • $\begingroup$ A nice explanation of relativistic space travel, but it doesn't deal with the speeds of generation ships. $\endgroup$ – a4android Oct 6 '17 at 2:53
  • $\begingroup$ @anon: temporal dilation is even more fun than that. As you approach the speed of light (or fall into a really deep gravity well) 1 second of time on the ship tends towards infinity elsewhere, so if you go fast enough you don’t need a generation ship: your original crew will be just fine. $\endgroup$ – Joe Bloggs Oct 6 '17 at 6:43
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Another non-answer to the question as it was asked, but perhaps I can help the original poster anyway. There are two related problems with interstellar travel.

It is difficult to accelerate to a high speed. Just how fast the ship can get depends on the drive technology and the fuel or reaction mass percentage. In theory, lightspeed is the limit. In practice, the possible delta-V is much lower. The Atomic Rockets page is a great introduction to different technologies.

It is difficult to crew a multi-decade mission. Again, generation ships are only one option, and perhaps not the best.

  • Robot probes, perhaps with an AI, a mind emulation, or a brain scan if such technologies turn out to be feasible.
  • Suspended animation, if humans can survive it.
  • An artificial womb to raise crew from frozen eggs.

All those are wildly impractical right now, but so is the life support system for a generation ship. Consider how the Biosphere 2 experiments ended.

So back to the original question: How fast can a generation ship be? No faster or slower than any of the other payload concepts; if you have the technology to get an AI probe to 0.3 c (for instance), more of the same (bigger engines, bigger tanks) will get a generation ship to 0.3 c as well.

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I did the calculations a couple weeks ago. Generation ships are slow and sort of dumb, and will never be used in our grand colonization of the universe. What you need are relativistic ships. With an acceleration of 1.25 Gs(12.25 m/p/s, you can reach Proxima Centauri with a ship-time of about 1126 days, or over 3 years. You can do this for distances as large as you want. Even to Andromeda, without it becoming a generation ship. Here's a handy calculator that I used a lot: http://gregsspacecalculations.blogspot.com/p/blog-page.html?a=9.80665&b=45006225.31625569&c=329519569.220615

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  • $\begingroup$ While this answer points the advantages of relativistic space travel, it doesn't address the sort of speeds typical of generation ships. $\endgroup$ – a4android Oct 6 '17 at 2:52
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    $\begingroup$ I don't think this answer deserved the downvotes it got. Certainly not without an explanation from the downvoters. This will help the poster improve their answers in future. $\endgroup$ – a4android Oct 6 '17 at 4:33
  • $\begingroup$ Thank you for the link to relativistic space travel calculator. This will be very useful. $\endgroup$ – a4android Oct 6 '17 at 5:18

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